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2 years ago

Solve (x + 2 < 5) ∩ (x - 7 > -6).

Mathematics

2 answers:

IceJOKER [234]2 years ago

8 0

Answer:

Assuming b

Step-by-step explanation:

the person above said it was b so

garri49 [273]2 years ago

3 0

Let $A=x+2\lt5, B=x-7\gt6$ .

Simplifying both you get $A=x\lt3,B=x\gt1$ .

The set conjunction is $A\cap B=1\lt x\lt3$ .

So the answer is B.

Hope this helps.

You might be interested in

The answer to this equation

12345 [234]

Answer:

x=3

Step-by-step explanation:

We are given the equation

$log5x=log(2x+9)$

This can be rewritten as

$log5x-log(2x+9)=0$

Now using the quotient rule for logarithms we can combine these two

$log(\frac{5x}{2x+9} )=0$

Next we can remove the log by using an inverse operation

$10^{log(\frac{5x}{2x+9} )} =10^0\\\\\frac{5x}{2x+9}=1$

Now we can solve for x

$\frac{5x}{2x+9}=1\\\\5x=2x+9\\\\3x=9\\\\x=3$

4 0

3 years ago

A survey of 500 high school students was taken to determine their favorite chocolate candy. Of the 500 students surveyed, 150 li

Anika [276]

Answer:

N(AUC∩B') = 121

The number of students that like Reese's Peanut Butter Cups or Snickers, but not Twix is 121

Step-by-step explanation:

Let A represent snickers, B represent Twix and C represent Reese's Peanut Butter Cups.

Given;

N(A) = 150

N(B) = 204

N(C) = 206

N(A∩B) = 75

N(A∩C) = 100

N(B∩C) = 98

N(A∩B∩C) = 38

N(Total) = 500

How many students like Reese's Peanut Butter Cups or Snickers, but not Twix;

N(AUC∩B')

This can be derived by first finding;

N(AUC) = N(A) + N(C) - N(A∩C)

N(AUC) = 150+206-100 = 256

Also,

N(A∩B U B∩C) = N(A∩B) + N(B∩C) - N(A∩B∩C) = 75 + 98 - 38 = 135

N(AUC∩B') = N(AUC) - N(A∩B U B∩C) = 256-135 = 121

N(AUC∩B') = 121

The number of students that like Reese's Peanut Butter Cups or Snickers, but not Twix is 121

See attached venn diagram for clarity.

The number of students that like Reese's Peanut Butter Cups or Snickers, but not Twix is the shaded part

6 0

2 years ago

Name a fourth point in plane TUY.<br> x<br> Y<br> W<br> Z

Elan Coil [88]

Answer:

Step-by-step explanation:

6 0

3 years ago

5. Which polygon is always regular?

Feliz [49]

Square because it's sides and angles are always congruent with eachother

7 0

2 years ago

If it took Carlos 30 minutes to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 mi

Ivanshal [37]

Answer:

1) No

2) Yes

Step-by-step explanation:

Given : If it took Carlos 30 minutes to cycle from his house to the library yesterday.

To find : Was the distance that he cycled greater than 6 miles?

Solution :

The relation between speed , distance and time is

$\text{Distance}=\text{Speed}\times \text{Time}$

1) The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.

Speed = 16 feet per second

Converting into miles, $s=\frac{16}{5280}$

Time = 30 minute

Converting into seconds, $t=30\times 60$

The distance he covered is

$\text{Distance}=\frac{16}{5280}\times30\times 60$

$\text{Distance}=5.45\text{ miles}$

No, the distance that he cycled is not greater than 6 miles.

2) The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second.

Speed = 18 feet per second

Converting into miles, $s=\frac{18}{5280}$

Time = 30 minute

Converting into seconds, $t=30\times 60$

The distance he covered is

$\text{Distance}=\frac{18}{5280}\times30\times 60$

$\text{Distance}=6.13\text{ miles}$

Yes, the distance that he cycled is greater than 6 miles.

6 0

3 years ago